the formula's = [n(n+1)]2 is used to find the sum of the first natural numbers. find the sum of the first 18 natural numbers.

Let S n = 1+2+3+4+...+n This series is an A.P. Here a=1, d=1, l = t n = n 2. To find the sum to squares of first n natural numbers. or..

1. To find the sum of first n natural numbers. ..

A set of numbers arranged in a definite order according to some definite rule is called a sequence. A sequence is a function whose domain is the set N of natural numbers. Indicated sum of the terms in a sequence is called a series. The r..

of (a + b) n and is given by - If n is an odd natural number, then there are two middle terms in the expansion of (a + b)n and are given by i) The sum of all binomial coefficients in the expansion of (1+x) n is 2..

Step 1: Factor pairs of the last term are (9,-2); (-6,3); (-18,1);(-9,2);(6,-3); (18,-1). Step 2: The pair of factors whose sum is equal to the co-efficient of the middle term is (-6,3). Step 3: Rewrite the expression using thes..

for every natural number n. In fact, this conjecture is valid and we establish it by using the principle of mathematical inducti..

For any natural number n, prove tha..

Let n N and P(n) denote a certain statement or formula or theorem. Then P(n) holds good for every natural number n if (i) it holds for n = 1 and (ii) it holds for n = k+1 whenever..

Let n N and P(n) denote a certain statement or formula or theorem. Then P(n) holds good for every natural number n if (i) it holds for n = 1 and (ii) it holds for n = k+..

A set of numbers arranged in a definite order according to some definite rule is called a sequence. or A sequence is a function whose domain is the set N of natural numbers. It is customary to denote a sequence by a letter 'a' and the image a(n) or..